Slowly rotating super-compact Schwarzschild stars

TL;DR

This paper investigates slowly rotating super-compact Schwarzschild stars, revealing their properties near the gravastar limit and showing they can mimic Kerr black hole characteristics, offering insights into black hole alternatives.

Contribution

It extends Hartle's model to analyze slowly rotating Schwarzschild stars near the gravastar limit, demonstrating their rotational properties resemble Kerr black holes.

Findings

Angular velocity tends to zero in the gravastar limit.

Normalized moment of inertia approaches Kerr values.

Mass quadrupole moment approaches Kerr values.

Abstract

The Schwarzschild interior solution, or `Schwarzschild star', which describes a spherically symmetric homogeneous mass with constant energy density, shows a divergence in pressure when the radius of the star reaches the Schwarzschild-Buchdahl bound. Recently Mazur and Mottola showed that this divergence is integrable through the Komar formula, inducing non-isotropic transverse stresses on a surface of some radius $R_{0}$. When this radius approaches the Schwarzschild radius $R_{s}=2M$, the interior solution becomes one of negative pressure evoking a de Sitter spacetime. This gravitational condensate star, or gravastar, is an alternative solution to the idea of a black hole as the ultimate state of gravitational collapse. Using Hartle's model to calculate equilibrium configurations of slowly rotating masses, we report results of surface and integral properties for a Schwarzschild star in the very little studied region $R_{s}<R<(9/8)R_{s}$. We found that in the gravastar limit, the angular velocity of the fluid relative to the local inertial frame tends to zero, indicating rigid rotation. Remarkably, the normalized moment of inertia $I/MR^2$ and the mass quadrupole moment $Q$ approach to the corresponding values for the Kerr metric to second order in $\Omega$. These results provide a solution to the problem of the source of a slowly rotating Kerr black hole.